{"id":"https://openalex.org/W1972283993","doi":"https://doi.org/10.1137/130925311","title":"A Hessian-Based Method for Uncertainty Quantification in Global Ocean State Estimation","display_name":"A Hessian-Based Method for Uncertainty Quantification in Global Ocean State Estimation","publication_year":2014,"publication_date":"2014-01-01","ids":{"openalex":"https://openalex.org/W1972283993","doi":"https://doi.org/10.1137/130925311","mag":"1972283993"},"language":"en","primary_location":{"id":"doi:10.1137/130925311","is_oa":true,"landing_page_url":"https://doi.org/10.1137/130925311","pdf_url":null,"source":{"id":"https://openalex.org/S165512578","display_name":"SIAM Journal on Scientific Computing","issn_l":"1064-8275","issn":["1064-8275","1095-7197"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Scientific Computing","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://doi.org/10.1137/130925311","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5007411474","display_name":"Alexander G. Kalmikov","orcid":null},"institutions":[{"id":"https://openalex.org/I63966007","display_name":"Massachusetts Institute of Technology","ror":"https://ror.org/042nb2s44","country_code":"US","type":"education","lineage":["https://openalex.org/I63966007"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Alexander G. Kalmikov","raw_affiliation_strings":["Department of Earth, Atmospheric, and Planetary Sciences, Massachusetts Institute of Technol-ogy, Cambridge, MA 02139"],"affiliations":[{"raw_affiliation_string":"Department of Earth, Atmospheric, and Planetary Sciences, Massachusetts Institute of Technol-ogy, Cambridge, MA 02139","institution_ids":["https://openalex.org/I63966007"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5058612077","display_name":"Patrick Heimbach","orcid":"https://orcid.org/0000-0003-3925-6161"},"institutions":[{"id":"https://openalex.org/I63966007","display_name":"Massachusetts Institute of Technology","ror":"https://ror.org/042nb2s44","country_code":"US","type":"education","lineage":["https://openalex.org/I63966007"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Patrick Heimbach","raw_affiliation_strings":["Department of Earth, Atmospheric, and Planetary Sciences, Massachusetts Institute of Technol-ogy, Cambridge, MA 02139"],"affiliations":[{"raw_affiliation_string":"Department of Earth, Atmospheric, and Planetary Sciences, Massachusetts Institute of Technol-ogy, Cambridge, MA 02139","institution_ids":["https://openalex.org/I63966007"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5058612077"],"corresponding_institution_ids":["https://openalex.org/I63966007"],"apc_list":null,"apc_paid":null,"fwci":6.7322,"has_fulltext":false,"cited_by_count":70,"citation_normalized_percentile":{"value":0.96838728,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":94,"max":100},"biblio":{"volume":"36","issue":"5","first_page":"S267","last_page":"S295"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10255","display_name":"Oceanographic and Atmospheric Processes","score":0.9997000098228455,"subfield":{"id":"https://openalex.org/subfields/1910","display_name":"Oceanography"},"field":{"id":"https://openalex.org/fields/19","display_name":"Earth and Planetary Sciences"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T10255","display_name":"Oceanographic and Atmospheric Processes","score":0.9997000098228455,"subfield":{"id":"https://openalex.org/subfields/1910","display_name":"Oceanography"},"field":{"id":"https://openalex.org/fields/19","display_name":"Earth and Planetary Sciences"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10029","display_name":"Climate variability and models","score":0.9973999857902527,"subfield":{"id":"https://openalex.org/subfields/2306","display_name":"Global and Planetary Change"},"field":{"id":"https://openalex.org/fields/23","display_name":"Environmental Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10466","display_name":"Meteorological Phenomena and Simulations","score":0.9973000288009644,"subfield":{"id":"https://openalex.org/subfields/1902","display_name":"Atmospheric Science"},"field":{"id":"https://openalex.org/fields/19","display_name":"Earth and Planetary Sciences"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/hessian-matrix","display_name":"Hessian matrix","score":0.913062334060669},{"id":"https://openalex.org/keywords/jacobian-matrix-and-determinant","display_name":"Jacobian matrix and determinant","score":0.6856457591056824},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5201040506362915},{"id":"https://openalex.org/keywords/uncertainty-quantification","display_name":"Uncertainty quantification","score":0.49730828404426575},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.47844627499580383},{"id":"https://openalex.org/keywords/adjoint-equation","display_name":"Adjoint equation","score":0.46547481417655945},{"id":"https://openalex.org/keywords/data-assimilation","display_name":"Data assimilation","score":0.4648631513118744},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4525616765022278},{"id":"https://openalex.org/keywords/covariance","display_name":"Covariance","score":0.4505404531955719},{"id":"https://openalex.org/keywords/eigenvalues-and-eigenvectors","display_name":"Eigenvalues and eigenvectors","score":0.4291001558303833},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.4050149917602539},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3388977646827698},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.10228639841079712}],"concepts":[{"id":"https://openalex.org/C203616005","wikidata":"https://www.wikidata.org/wiki/Q620495","display_name":"Hessian matrix","level":2,"score":0.913062334060669},{"id":"https://openalex.org/C200331156","wikidata":"https://www.wikidata.org/wiki/Q506041","display_name":"Jacobian matrix and determinant","level":2,"score":0.6856457591056824},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5201040506362915},{"id":"https://openalex.org/C32230216","wikidata":"https://www.wikidata.org/wiki/Q7882499","display_name":"Uncertainty quantification","level":2,"score":0.49730828404426575},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.47844627499580383},{"id":"https://openalex.org/C165551260","wikidata":"https://www.wikidata.org/wiki/Q4428962","display_name":"Adjoint equation","level":3,"score":0.46547481417655945},{"id":"https://openalex.org/C24552861","wikidata":"https://www.wikidata.org/wiki/Q2670177","display_name":"Data assimilation","level":2,"score":0.4648631513118744},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4525616765022278},{"id":"https://openalex.org/C178650346","wikidata":"https://www.wikidata.org/wiki/Q201984","display_name":"Covariance","level":2,"score":0.4505404531955719},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.4291001558303833},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.4050149917602539},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3388977646827698},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.10228639841079712},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.0},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.0},{"id":"https://openalex.org/C153294291","wikidata":"https://www.wikidata.org/wiki/Q25261","display_name":"Meteorology","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1137/130925311","is_oa":true,"landing_page_url":"https://doi.org/10.1137/130925311","pdf_url":null,"source":{"id":"https://openalex.org/S165512578","display_name":"SIAM Journal on Scientific Computing","issn_l":"1064-8275","issn":["1064-8275","1095-7197"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Scientific Computing","raw_type":"journal-article"},{"id":"pmh:oai:dspace.mit.edu:1721.1/92547","is_oa":true,"landing_page_url":"http://hdl.handle.net/1721.1/92547","pdf_url":null,"source":{"id":"https://openalex.org/S4306400425","display_name":"DSpace@MIT (Massachusetts Institute of Technology)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I63966007","host_organization_name":"Massachusetts Institute of Technology","host_organization_lineage":["https://openalex.org/I63966007"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-nc","license_id":"https://openalex.org/licenses/cc-by-nc","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Society for Industrial and Applied Mathematics","raw_type":"http://purl.org/eprint/type/JournalArticle"}],"best_oa_location":{"id":"doi:10.1137/130925311","is_oa":true,"landing_page_url":"https://doi.org/10.1137/130925311","pdf_url":null,"source":{"id":"https://openalex.org/S165512578","display_name":"SIAM Journal on Scientific Computing","issn_l":"1064-8275","issn":["1064-8275","1095-7197"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Scientific Computing","raw_type":"journal-article"},"sustainable_development_goals":[{"display_name":"Life below water","id":"https://metadata.un.org/sdg/14","score":0.8700000047683716}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":45,"referenced_works":["https://openalex.org/W1500745827","https://openalex.org/W1506690472","https://openalex.org/W1513885519","https://openalex.org/W1514740718","https://openalex.org/W1541503520","https://openalex.org/W1576347883","https://openalex.org/W1580960545","https://openalex.org/W1583174948","https://openalex.org/W1585773866","https://openalex.org/W1964386634","https://openalex.org/W1966717343","https://openalex.org/W1970273374","https://openalex.org/W1971621572","https://openalex.org/W1971800650","https://openalex.org/W1996852196","https://openalex.org/W2017583417","https://openalex.org/W2017755281","https://openalex.org/W2022264564","https://openalex.org/W2023103251","https://openalex.org/W2052809541","https://openalex.org/W2057313876","https://openalex.org/W2074836377","https://openalex.org/W2082261407","https://openalex.org/W2082585997","https://openalex.org/W2086683242","https://openalex.org/W2095921725","https://openalex.org/W2097790278","https://openalex.org/W2105572579","https://openalex.org/W2111976683","https://openalex.org/W2114466308","https://openalex.org/W2116960696","https://openalex.org/W2118055195","https://openalex.org/W2124838643","https://openalex.org/W2127946544","https://openalex.org/W2130844535","https://openalex.org/W2134380122","https://openalex.org/W2141771173","https://openalex.org/W2155290594","https://openalex.org/W2159883344","https://openalex.org/W2169043969","https://openalex.org/W2179229003","https://openalex.org/W2180274418","https://openalex.org/W2323143762","https://openalex.org/W2797638056","https://openalex.org/W3015681226"],"related_works":["https://openalex.org/W2611031068","https://openalex.org/W1704347466","https://openalex.org/W4283017538","https://openalex.org/W1545275724","https://openalex.org/W2802707792","https://openalex.org/W3048332761","https://openalex.org/W2350095335","https://openalex.org/W2544528198","https://openalex.org/W2039064215","https://openalex.org/W1531770813"],"abstract_inverted_index":{"Derivative-based":[0],"methods":[1],"are":[2,64,82,106,224],"developed":[3],"for":[4,22,226,234],"uncertainty":[5,177,212,221],"quantification":[6],"(UQ)":[7],"in":[8,51,153],"large-scale":[9],"ocean":[10],"state":[11],"estimation.":[12],"The":[13,40,80,186],"estimation":[14],"system":[15],"is":[16,36,43,139,161,193],"based":[17],"on":[18],"the":[19,29,58,68,71,89,104,116,136,147,154,165,171,175,180,183,189,209,211,216],"adjoint":[20,131,150],"method":[21],"solving":[23],"a":[24,52,128],"least-squares":[25],"optimization":[26],"problem,":[27],"whereby":[28],"state-of-the-art":[30],"MIT":[31],"general":[32],"circulation":[33],"model":[34,90,125],"(MITgcm)":[35],"fit":[37],"to":[38,45,163,202],"observations.":[39,217],"UQ":[41],"framework":[42],"applied":[44,162],"quantify":[46],"Drake":[47,92],"Passage":[48,93],"transport":[49],"uncertainties":[50,232,237],"global":[53],"idealized":[54],"barotropic":[55],"configuration":[56],"of":[57,70,88,103,110,115,120,122,135,149,170,182,188],"MITgcm.":[59],"Large":[60],"error":[61],"covariance":[62],"matrices":[63],"evaluated":[65],"by":[66,95,108,195,205,215],"inverting":[67],"Hessian":[69,137,172,191],"misfit":[72,190],"function":[73],"using":[74],"matrix-free":[75],"numerical":[76],"linear":[77],"algebra":[78],"algorithms.":[79],"covariances":[81],"projected":[83],"onto":[84,238],"target":[85,240],"output":[86],"quantities":[87],"(here":[91],"transport)":[94],"Jacobian":[96],"transformations.":[97],"First":[98],"and":[99,168,179,219,229,233],"second":[100,155],"derivative":[101,156],"codes":[102],"MITgcm":[105],"generated":[107],"means":[109],"algorithmic":[111],"differentiation":[112],"(AD).":[113],"Transpose":[114],"chain":[117],"rule":[118],"product":[119],"Jacobians":[121],"elementary":[123],"forward":[124,220],"operations":[126],"implements":[127],"computationally":[129],"efficient":[130],"code.":[132],"Computational":[133],"complexity":[134],"code":[138],"reduced":[140,194],"via":[141],"forward-over-reverse":[142],"mode":[143],"AD,":[144],"which":[145],"preserves":[146],"efficiency":[148],"checkpointing":[151],"schemes":[152,223],"calculation.":[157],"A":[158],"Lanczos":[159],"algorithm":[160],"extract":[164],"leading":[166],"eigenvectors":[167],"eigenvalues":[169],"matrix,":[173],"representing":[174],"constrained":[176],"patterns":[178],"inverse":[181],"corresponding":[184],"uncertainties.":[185],"dimensionality":[187],"inversion":[192],"omitting":[196],"its":[197],"nullspace":[198],"(as":[199],"an":[200],"alternative":[201],"suppressing":[203],"it":[204],"regularization),":[206],"excluding":[207],"from":[208],"computation":[210],"subspace":[213],"unconstrained":[214],"Inverse":[218],"propagation":[222],"designed":[225],"assimilating":[227],"observation":[228],"control":[230],"variable":[231],"projecting":[235],"these":[236],"oceanographic":[239],"quantities.":[241]},"counts_by_year":[{"year":2026,"cited_by_count":3},{"year":2024,"cited_by_count":6},{"year":2023,"cited_by_count":12},{"year":2022,"cited_by_count":7},{"year":2021,"cited_by_count":9},{"year":2020,"cited_by_count":4},{"year":2019,"cited_by_count":6},{"year":2018,"cited_by_count":2},{"year":2017,"cited_by_count":3},{"year":2016,"cited_by_count":7},{"year":2015,"cited_by_count":11}],"updated_date":"2026-03-20T23:20:44.827607","created_date":"2025-10-10T00:00:00"}
